The $1,018 (£740) trainers, which feature an inverted cross, a pentagram and the words "Luke 10:18", were made using modified Nike Air Max 97s.
MSCHF released 666 pairs of the shoes on Monday on its app and says they sold out in less than a minute.
Nike is claiming the collective infringed its trademark.
The black and red shoes were "dropped" by MSCHF on Monday, coinciding with the launch of Lil Nas X's latest song Montero (Call Me By Your Name), which debuted on YouTube last Friday.
In the music video, the rapper is seen sliding down a stripper pole from heaven to hell, wearing a pair of the trainers.
The imagery and the shoes reference the Bible verse Luke 10:18 - "So He told them, 'I saw Satan fall like lightning from heaven'."
Each shoe features a signature Nike air bubble cushioning sole, containing 60 cubic centimetres (2.03 fluid ounces) of red ink and a single drop of human blood, donated by members of the art collective.
The sports shoe giant says in a filing with the US District Court for the Eastern District of New York that it does not approve or authorise the customised Satan Shoes.
Nike is asking the court to stop MSCHF from selling the shoes and prevent them from using its famous Swoosh design mark.
"MSCHF and its unauthorised Satan Shoes are likely to cause confusion and dilution and create an erroneous association between MSCHF's products and Nike," the sports shoe giant says in the lawsuit.
"In fact, there is already evidence of significant confusion and dilution occurring in the marketplace, including calls to boycott Nike in response to the launch of MSCHF's Satan Shoes, based on the mistaken belief that Nike has authorised or approved this product."
The lawsuit cites a tweet by popular shoe influencer @Saint from last Friday, which teased the upcoming release of the shoes and drummed up publicity over the weekend on social media and in the media in the US.
Some Conservatives, including South Dakota Governor Kristi Noem, and some religious followers, took offence at the controversial design of the shoes and criticised Lil Nas X and MSCHF on Twitter.